Research Article
On the Effectiveness of Nature-Inspired Metaheuristic Algorithms for Performing Phase Equilibrium Thermodynamic Calculations
Table 4
Minimum NFE for the average best value to reach 1E-3, 1E-4, 1E-5, 1E-6, and 1E-7 from the known global minimum.
| Metaheuristic | | Phase equilibrium thermodynamic problem | T7 | T8 | T9 | G4 | G6 | G7 | G8 | R4 | R7 |
| MAKHA | 1E-3 | | 2164 | 601 | 121 | 301 | 481 | 4328 | | 10845 | 1E-4 | | 45444 | 1803 | 121 | 602 | 4329 | 39493 | | 40006 | 1E-5 | | | | 484 | 903 | | | | 40488 | 1E-6 | | | | 2299 | 1806 | | | | 40729 | 1E-7 | | | | 2783 | | | | | 41211 |
| IFA | 1E-3 | | 8820 | 1400 | 40 | 400 | 1600 | 19980 | 17300 | 9440 | 1E-4 | | 24840 | 5200 | 40 | 3500 | 18880 | 36720 | | 14480 | 1E-5 | | 39600 | | 1040 | 9000 | | 52560 | | 20080 | 1E-6 | | | | | 15400 | | 73260 | | 25040 | 1E-7 | | | | | | | | | 30160 |
| CMAES | 1E-3 | | 3961 | 201 | 41 | 101 | 161 | 3961 | | | 1E-4 | | 5761 | 201 | 41 | 101 | 2721 | 5401 | | | 1E-5 | | 7381 | 5801 | | 101 | 4801 | 7021 | | | 1E-6 | | | | | 101 | 8641 | 8821 | | | 1E-7 | | | | | 2401 | 11681 | 10621 | | |
| ABC | 1E-3 | 9840 | 8010 | 4100 | 60 | 850 | 2480 | 6570 | 9750 | 9560 | 1E-4 | | 12150 | 9700 | 60 | 1950 | 7920 | 11790 | 24959 | 48236 | 1E-5 | | 17010 | 21500 | 1220 | 3850 | 34644 | 19530 | | | 1E-6 | | | 58104 | 12460 | 8650 | | 27990 | | | 1E-7 | | | | 33092 | | | 41850 | | |
| BA | 1E-3 | | 1980 | 400 | 80 | 200 | 320 | 1800 | | | 1E-4 | | 2340 | 400 | 80 | 200 | 5760 | 3240 | | | 1E-5 | | | 43200 | 6960 | 400 | | 16920 | | | 1E-6 | | | | 8400 | 3700 | | | | | 1E-7 | | | | 8440 | | | | | |
| MCSS | 1E-3 | 87520 | 35640 | 800 | 40 | 400 | 640 | 26460 | | 21200 | 1E-4 | | 80820 | 6200 | 40 | 1100 | 36800 | 104400 | | 34160 | 1E-5 | | 178920 | 78000 | 3520 | 3300 | 157600 | | | 64320 | 1E-6 | | | | 7880 | 11000 | | | | | 1E-7 | | | | 9120 | 49600 | | | | |
| CS | 1E-3 | 41440 | 17460 | 7400 | 120 | 1700 | 7840 | 22140 | 16100 | 10640 | 1E-4 | 79200 | 35100 | 11800 | 120 | 4100 | 26400 | 44820 | 30900 | 17680 | 1E-5 | 109280 | 61380 | 57400 | 1160 | 5500 | 52960 | 74700 | 50300 | 30000 | 1E-6 | 132640 | | 93400 | 3480 | 6700 | 93280 | 112500 | 70300 | 39760 | 1E-7 | 155040 | | 131400 | 4440 | 24100 | 140000 | 152820 | 87300 | 53840 |
| BBPSO | 1E-3 | | 9900 | 2800 | 40 | 600 | 1760 | 7380 | | 9440 | 1E-4 | | 14040 | 7400 | 40 | 1700 | 12640 | 11340 | | 17920 | 1E-5 | | 18720 | 21600 | 920 | 3300 | | 15300 | | 21440 | 1E-6 | | | | 2200 | 6000 | | 19080 | | 23360 | 1E-7 | | | | 5120 | | | 22500 | | 28400 |
|
|